An actuator of the type described above, which is intended for the actuation of a selector shaft of an automated transmission in a motor vehicle, is known from practice. It comprises as a drive an electric motor with a stator comprising a winding and a permanent-magnet rotor working together therewith. On the periphery of the rotor a row of permanent-magnet segments is disposed which extends in the peripheral direction and has alternating north and south poles. Disposed on the electric motor to register the relative position between the rotor and the stator is an incremental encoder which comprises, on the stator, several Hall sensors which are spaced from one another in the peripheral direction and which detect the magnetic field of the permanent-magnet segments passing by. The incremental encoder is connected to a control device which evaluates the measurement signals of the Hall sensors and commutates the winding as a function of the position of the rotor relative to the stator. The control device is disposed in a housing spatially separated from the incremental encoder and is connected via electrical cable to the incremental encoder. So that the selector shaft is not displaced in an uncontrolled manner when there is a failure or malfunction of the incremental encoder, the control device comprises a device for checking the plausibility of the position measurement signal. On the occurrence of an implausible signal state the power supply to the electric motor is disconnected with the aid of the control device. So that the electric motor can be produced economically and has low weight and compact dimensions, it is dimensioned so that it is indeed suitable for a short-time load but not for long-term operation. So that the electric motor nonetheless does not overheat in the operational states occurring in practice, the dimensioning is based on unfavorable conditions of operation, such as, for example, driving in mountainous terrain with a fully loaded motor vehicle and high ambient temperature. These conditions of operation occur only very rarely in the normal operation of the motor vehicle so that the electric motor is over-dimensioned for the loads customarily occurring during the operation of the motor vehicle.